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Funktsional'nyi Analiz i ego Prilozheniya, 2023, Volume 57, Issue 2, Pages 3–17
DOI: https://doi.org/10.4213/faa4056
(Mi faa4056)
 

Multipliers for the Calderón construction

E. I. Berezhnoi

P. G. Demidov Yaroslavl State University, Faculty of Mathematics
References:
Abstract: On the basis of a new approach to the Calderón construction $X_0^{\theta} X_1^{1-\theta}$ for ideal spaces $X_0$ and $X_1$ and a parameter $\theta \in [0,1]$, final results concerning a description of multipliers spaces are obtained. In particular, it is shown that if ideal spaces $X_0$ and $X_1$ have the Fatou property, then $M(X_0^{\theta_0} X_1^{1-\theta_0}\,{\to}\,X_0^{\theta_1} X_1^{1-\theta_1}) = M(X_1^{\theta_1 - \theta_0} \to X_0^{\theta_1 -\theta_0})$ for $0 <\theta_0 <\theta_1 <1$. Due to the absence of constraints on the ideal spaces $X_0$ and $X_1$, the obtained results apply to a large class of ideal spaces.
Keywords: ideal Banach space, Calderón construction, pointwise multiplier, local Morrey space.
Received: 02.10.2022
Revised: 07.02.2023
Accepted: 10.02.2023
English version:
Functional Analysis and Its Applications, 2023, Volume 57, Issue 2, Pages 87–98
DOI: https://doi.org/10.1134/S0016266323020016
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: E. I. Berezhnoi, “Multipliers for the Calderón construction”, Funktsional. Anal. i Prilozhen., 57:2 (2023), 3–17; Funct. Anal. Appl., 57:2 (2023), 87–98
Citation in format AMSBIB
\Bibitem{Ber23}
\by E.~I.~Berezhnoi
\paper Multipliers for the Calder\'on construction
\jour Funktsional. Anal. i Prilozhen.
\yr 2023
\vol 57
\issue 2
\pages 3--17
\mathnet{http://mi.mathnet.ru/faa4056}
\crossref{https://doi.org/10.4213/faa4056}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4547037}
\transl
\jour Funct. Anal. Appl.
\yr 2023
\vol 57
\issue 2
\pages 87--98
\crossref{https://doi.org/10.1134/S0016266323020016}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85180902213}
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    Функциональный анализ и его приложения Functional Analysis and Its Applications
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